Series representation of x^2/(a^3-x^3)

First I tried breaking this up into partial fractions, then I realized I'm not very good at doing partial fractions... But I think I found another path that maybe I'm supposed to use:

Consider that:

I think this somehow relates to the integral of the alternating geometric series (switching variable for clarity):

I know I can integrate the terms of the geometric series to get the natural log, but I also know I can't just plug , and now I'm not sure what to do. Am I headed down the right tree or barking up the wrong path? Do I need to return to the partial fractions approach instead?

log(1+x) can be easily expanded. it was somewht like this log(1+x)=1+x^2/2-x^3/3+.....(i am not sure please correct me if i am wrong). since u have got an expression in log u should be able to expand it......

First I tried breaking this up into partial fractions, then I realized I'm not very good at doing partial fractions... But I think I found another path that maybe I'm supposed to use:

Consider that:

I think this somehow relates to the integral of the alternating geometric series (switching variable for clarity):

I know I can integrate the terms of the geometric series to get the natural log, but I also know I can't just plug , and now I'm not sure what to do. Am I headed down the right tree or barking up the wrong path? Do I need to return to the partial fractions approach instead?

Thanks again for any help,

Brian

The integration method works ok (don't forget to differentiate).

How about this though? . Now, just for the sake of clarity try calling . Look familiar?

log(1+x) can be easily expanded. it was somewht like this log(1+x)=1+x^2/2-x^3/3+.....(i am not sure please correct me if i am wrong). since u have got an expression in log u should be able to expand it......